Rigoberto Juarez-Salazar

Theory and algorithms of an efficient fringe analysis technology for automatic measurement applications.

Some advances in fringe analysis technology for phase computing are presented. A full scheme for phase evaluation, applicable to automatic applications, is proposed. The proposal consists of: a fringe-pattern normalization method, Fourier fringe-normalized analysis, generalized phase-shifting processing for inhomogeneous nonlinear phase shifts and spatiotemporal visibility, and a phase-unwrapping method by a rounding-least-squares approach. The theoretical principles of each algorithm are given. Numerical examples and an experimental evaluation are presented.

Generalized phase-shifting algorithm for inhomogeneous phase shift and spatio-temporal fringe visibility variation

A cascade least-squares scheme for wrapped phase extraction using two or more phase-shifted fringe-patterns with unknown and inhomogeneous surface phase shift is proposed. This algorithm is based on the parameter estimation approach to process fringe-patterns where, except for the interest phase distribution that is a function of the space only, all other parameters are functions of both space and time. Computer simulations and experimental results show that phase computing is possible even when an inhomogeneous phase shift is induced by nonlinearity of the piezoelectric materials or miscalibrated phase shifters. The algorithms features and its operating conditions will been discussed. Due to the useful properties of this algorithm such as the robustness, computational efficiency, and user-free execution, this proposal could be used in automatic applications.

Fourier normalized-fringe analysis by zero-order spectrum suppression using a parameter estimation approach

Abstract. The simple filtering procedure, high spatial resolution, and low computation time benefits of Fourier normalized-fringe analysis are verified. For this, both the fringe-pattern normalization method by parameter estimation using the least squares method and the standard Fourier transform method are implemented. This proposal, or any Fourier normalized-fringe analysis scheme, has the advantage that the filter’s properties are not very critical because the zero-order spectrum is suppressed by the normalization stage. Then, the simple half-plane filter is applied in the filtering procedure which, in addition, increases the spatial resolution. Both a computer simulation and the experimental results show the functionality and feasibility of the suggested scheme.

Phase-unwrapping algorithm by a rounding-least-squares approach

Abstract. A simple and efficient phase-unwrapping algorithm based on a rounding procedure and a global least-squares minimization is proposed. Instead of processing the gradient of the wrapped phase, this algorithm operates over the gradient of the phase jumps by a robust and noniterative scheme. Thus, the residue-spreading and over-smoothing effects are reduced. The algorithm’s performance is compared with four well-known phase-unwrapping methods: minimum cost network flow (MCNF), fast Fourier transform (FFT), quality-guided, and branch-cut. A computer simulation and experimental results show that the proposed algorithm reaches a high-accuracy level than the MCNF method by a low-computing time similar to the FFT phase-unwrapping method. Moreover, since the proposed algorithm is simple, fast, and user-free, it could be used in metrological interferometric and fringe-projection automatic real-time applications.

Camera calibration by multiplexed phase encoding of coordinate information.

A simple camera calibration method based on the principle of phase encoding and coordinate transformation is proposed. We use a reference coordinate frame encoded as a phase distribution by multiplexing the x and y directions. From this, we suggest a phase demodulation system. The coordinate transformation induced by the imaging is exploited to estimate the intrinsic and extrinsic camera parameters by using the least-squares method. Thus, a robust and noniterative estimation scheme is obtained. Simulations and experimental results show the feasibility of the proposal. Because of the potential for calibrating projectors, the proposed method could be used to calibrate fringe-projection systems.

Phase-shifting interferometry based on the lateral displacement of the light source.

A simple and inexpensive optical setup to phase-shifting interferometry is proposed. This optical setup is based on the Twyman-Green Interferometer where the phase shift is induced by the lateral displacement of the point laser source. A theoretical explanation of the induced phase by this alternative method is given. The experimental results are consistent with the theoretical expectations. Both, the phase shift and the wrapped phase are recovered by a generalized phase-shifting algorithm from two or more interferograms with arbitrary and unknown phase shift. The experimental and theoretical results show the feasibility of this unused phase-shifting technique.

Straightforward filtering to phase demodulation by a Fourier normalized-fringe approach

The fringe-pattern normalization method by parameter estimation is used to relieve the critical filters requirements in the Fourier transform method for phase demodulation. By the normalization procedure, the zero order spectrum is suppressed allowing a straightforward filtering in the Fourier transform method. Thus, the filtering procedure is carried out by the simple half-plane filter. The benefits of this Fourier normalized-fringe analysis scheme are tested by both computer simulation and optical experiments.

Automatic real-time generalized phase-shifting interferometry to process interferograms with spatio-temporal visibility

A faster and robust generalized phase-shifting interferometry suitable to automatic real-time applications is presented. The proposal is based on the parameter estimation by the least squares method. The algorithm can retrieve the wrapped phase from two or more phase shifted interferograms with unknown phase steps between 0 and π rad. Moreover, by the multiple or single parameter estimation approach of this algorithm, interferograms with variable visibility both spatial and temporally can be processed, overcoming the restrictions and drawbacks from usual variable spatial visibility approaches. By both computer simulation and a optical experiment, the algorithms feasibility is illustrated.

Stereo matching using adaptive windows and correlation filtering

Stereo matching is challenging due to the presence of perspective distortions and noise. Commonly, stereo matching algorithms utilize local matching techniques to determine the correspondence of two pixels of the same point in a scene. This work presents a stereo matching algorithm based on locally-adaptive windows and correlation filtering. The proposed algorithm estimates the disparity of each pixel by matching an adaptive sliding-window obtained from the left image in the right image of the stereo pair. Computer simulation results obtained with the proposed algorithm are analyzed and discussed by processing pairs of stereo images.

Homography estimation for camera document scanning applications

Rectangular shapes in observed scenes are transformed to quadrilaterals in resulting images due to perspective distortion. If the aspect ratio of the original rectangle is known, the associated homography can be computed directly and used for perspective correction. However, in camera document scanning applications, the aspect ratio of the imaged rectangle is unknown. In this work, a homography estimation method appropriate for document scanning applications is given. This method does not require a priori knowledge of the aspect ratio of the imaged rectangle nor a calibrated camera. The computational implementation is evaluated experimentally.